Question: For various values of k, form an k k matrix A by setting A = 2 * eye(k) - diag(ones(k - 1, 1), 1)

For various values of k, form an k × k matrix A by setting
A = 2 * eye(k) - diag(ones(k - 1, 1), 1) - diag(ones(k - 1, 1), -1)
In each case, compute the LU factorization of A and the determinant of A. If A is an n × n matrix of this form, what will its LU factorization be? What will its determinant be? Why must the matrix be positive definite?

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